CN115440382A - Blood flow numerical simulation method and device - Google Patents

Abstract

The application is applicable to the field of computational fluid mechanics, and provides a blood flow numerical simulation method. The method comprises the following steps: acquiring a three-dimensional model of a blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data comprises blood flow velocities at a plurality of target points in the three-dimensional model; the three-dimensional model includes a plurality of vessel regions; determining the resistance of an outlet in each blood vessel region according to the blood flow velocities of the plurality of target points and the pressure difference at the inlet of the three-dimensional model; determining the boundary condition of a fluid control equation of a blood vessel to be evaluated according to the blood flow velocity measurement data and the resistance of outlets in a plurality of blood vessel regions; and solving the fluid control equation according to the boundary conditions to obtain a blood flow numerical simulation result of the blood vessel to be evaluated. According to the method and the device, the resistance of the outlet in the blood vessel region is determined according to the blood flow velocity of the target point, the accuracy of the resistance of the outlet is improved, the boundary condition of the fluid control equation is determined according to the resistance of the outlet, and the accuracy of the blood flow numerical simulation result obtained by solving the equation is improved.

Description

Blood flow numerical simulation method and device

technical field

The application belongs to the technical field of computational fluid dynamics, and in particular relates to a blood flow numerical simulation method and device.

Background technique

The geometric shape, physiological conditions and biomechanics of blood vessels will affect the blood flow inside the blood vessels, and complex blood flow will cause some physiological changes in blood vessels, which are related to the occurrence and development of lesions. Therefore, hemodynamic simulation can provide an important reference for the prevention and treatment of cerebrovascular diseases.

At present, Computational Fluid Dynamics (CFD) method, as a commonly used hemodynamic quantitative analysis tool, has been widely used in hemodynamic simulation to evaluate the blood flow state inside the blood vessel. When using the CFD method to study the hydrodynamic properties of blood vessels, because the blood flow of the distal blood vessels cannot be measured one by one, and the existing method of determining the blood flow in the blood vessel based on the cross-sectional area of the blood vessel is not accurate enough, so the blood flow is used as the basis. When performing hemodynamic simulation, the blood flow simulation results are not accurate enough.

Contents of the invention

In view of this, the present application provides a method and device for numerical simulation of blood flow, which can improve the accuracy of numerical simulation results of blood flow in blood vessels.

In the first aspect, the embodiment of the present application provides a blood flow numerical simulation method, including:

Acquiring a three-dimensional model of the blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data includes blood flow velocity at multiple target points in the three-dimensional model; the three-dimensional model includes multiple blood vessel regions;

determining an outlet resistance in each of the vascular regions based on the blood flow velocity at the plurality of target points and the pressure difference at the inlet of the three-dimensional model;

determining the boundary conditions of the fluid control equation of the vessel to be evaluated according to the blood flow velocity measurement data and the outlet resistances in a plurality of the vessel regions;

Solving the fluid control equation according to the boundary conditions to obtain a blood flow numerical simulation result of the blood vessel to be evaluated.

According to the blood flow velocity of the target point and the pressure difference at the inlet of the three-dimensional model, the embodiment of the present application determines the outlet resistance in the blood vessel region, improves the accuracy of determining the outlet resistance, and determines the boundary of the fluid control equation according to the outlet resistance The conditions improve the accuracy of the blood flow numerical simulation results obtained by solving the fluid control equations.

In a possible implementation manner, the determining the outlet resistance in each of the blood vessel regions according to the blood flow velocity of the multiple target points and the pressure difference at the inlet of the three-dimensional model includes:

Obtaining the blood flow of each of the target points according to the blood flow velocity of each of the target points;

determining the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model according to the blood flow at multiple target points;

The outlet resistance of each of the blood vessel regions is determined according to the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model and the pressure difference at the inlet of the three-dimensional model.

In this embodiment of the present application, the proportion of blood flow in the blood vessel area is determined by the blood flow velocity at the target point, and the outlet resistance is determined according to the blood flow proportion and the pressure difference at the entrance of the three-dimensional model, which improves the accuracy of determining the outlet resistance of the blood vessel. sex.

In a possible implementation manner, the outlet in each of the blood vessel regions is determined according to the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model and the pressure difference at the inlet of the three-dimensional model resistance, including:

Obtaining the total resistance of the three-dimensional model according to the total blood flow of the three-dimensional model and the pressure difference at the inlet of the three-dimensional model;

For each of the blood vessel regions, according to the ratio of blood flow of the blood vessel region to the three-dimensional model and the total resistance of the three-dimensional model, the total resistance of the blood vessel region is obtained; and according to the total resistance of the blood vessel region The resistance and the cross-sectional dimension of the outlet in the vascular region obtain the resistance of the outlet in the vascular region.

In the embodiment of the present application, the total resistance of the three-dimensional model is determined first, and then the total resistance of the blood vessel area is allocated according to the blood flow ratio of the blood vessel area, and then the outlet resistance in the blood vessel area is obtained according to the cross-sectional size of the outlet in the blood vessel area, which improves the result. The accuracy of the outlet resistance in the vascular region.

In a possible implementation manner, the fluid control equation is the Navier-Stokes equation, the boundary conditions include an outlet boundary condition, and the The resistance of the outlet determines the boundary conditions of the fluid control equation of the blood vessel to be evaluated, including:

determining the parameters of the elastic chamber model corresponding to each outlet in each of the blood vessel regions according to the blood flow velocity measurement data and the resistance of the outlet in each of the blood vessel regions;

The outlet boundary condition of the fluid control equation is determined according to the parameters of the elastic chamber model corresponding to each outlet in the multiple blood vessel regions.

In the embodiment of the present application, the outlet is simulated through the elastic cavity model, and the outlet boundary condition of the fluid control equation is obtained after determining the parameters of the elastic cavity model, which improves the accuracy of the outlet boundary condition.

In a possible implementation manner, the solving the fluid control equation according to the boundary conditions includes:

dividing the three-dimensional model into a plurality of grids;

discretizing the fluid governing equations in the space domain and the time domain respectively according to the plurality of grids to obtain a sparse nonlinear system;

The sparse nonlinear system is solved according to the boundary conditions.

In the embodiment of the present application, the three-dimensional model is divided into multiple grids, and the fluid control equations are discretized according to the grids, thereby improving the solvability of the fluid control equations.

In a possible implementation manner, the solving the fluid control equation according to the boundary conditions includes:

The Newton-Krylov-Schwartz algorithm is used to solve the fluid governing equations.

In the embodiments of the present application, the Newton-Krylov-Schwartz algorithm is used to solve the fluid control equation, which improves the calculation efficiency when using a computer to solve the fluid control equation.

In a possible implementation manner, the acquiring the three-dimensional model of the blood vessel to be evaluated includes:

Acquiring tomographic image data of the vessel to be evaluated;

Acquiring a three-dimensional model of the blood vessel to be evaluated according to the tomographic image data.

In the embodiment of the present application, the three-dimensional model of the blood vessel to be evaluated is acquired through tomographic scanning image data, which improves the accuracy of the three-dimensional model of the blood vessel to be evaluated.

In the second aspect, the embodiment of the present application provides a blood flow numerical simulation device, including:

A first acquisition module, configured to acquire a three-dimensional model of a blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data includes blood flow velocity at multiple target points in the three-dimensional model; the three-dimensional model includes multiple blood vessel regions;

A first determining module, configured to determine the outlet resistance of each of the blood vessel regions according to the blood flow velocity of the plurality of target points and the pressure difference at the inlet of the three-dimensional model;

The second determination module is to determine the boundary conditions of the fluid control equation of the blood vessel to be evaluated according to the blood flow velocity measurement data and the resistance of outlets in a plurality of the blood vessel regions;

The second acquisition module is configured to solve the fluid control equation according to the boundary conditions, and acquire the blood flow numerical simulation results of the blood vessel to be evaluated.

In the third aspect, the embodiment of the present application provides a blood flow numerical simulation device, including a memory, a processor, and a computer program stored in the memory and operable on the processor, for implementing the above-mentioned first aspect methods in any possible implementation of .

In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, the readable storage medium is used to store a computer program, and when the computer program is executed by a processor, any possible solution of the above-mentioned first aspect can be realized. method in the implementation.

In the fifth aspect, the embodiment of the present application provides a computer program product, which, when the computer program is run on the blood flow numerical simulation device, causes the blood flow numerical simulation device to execute the method in any possible implementation manner of the first aspect above.

It can be understood that, for the beneficial effects of the above-mentioned second aspect to the fifth aspect, reference can be made to the relevant description in the above-mentioned first aspect, and details will not be repeated here.

Description of drawings

FIG. 1 is a schematic flow chart of a blood flow numerical simulation method provided in an embodiment of the present application;

2 is a schematic diagram of the division of the three-dimensional model region and the section of the blood vessel where the target point is provided in the embodiment of the present application;

Fig. 3 is the transcranial Doppler ultrasonogram provided by the embodiment of the present application;

Fig. 4 is a schematic flowchart of a method for determining the outlet resistance in a blood vessel region provided by an embodiment of the present application;

Fig. 5 is a schematic flow chart of determining the outlet resistance according to the blood flow ratio of each vascular region relative to the three-dimensional model provided by the embodiment of the present application;

Fig. 6 is a schematic diagram of the ternary elastic cavity model provided by the embodiment of the present application;

FIG. 7 is a schematic diagram of grid division provided by an embodiment of the present application;

Fig. 8 is a schematic block diagram of a blood flow numerical simulation device provided in an embodiment of the present application;

FIG. 9 is a schematic structural diagram of a blood flow numerical simulation device provided in an embodiment of the present application.

detailed description

In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

It should be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and/or components, but does not exclude one or more other Presence or addition of features, wholes, steps, operations, elements, components and/or collections thereof.

It should also be understood that the term "and/or" used in the description of the present application and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

As used in this specification and the appended claims, the term "if" may be construed, depending on the context, as "when" or "once" or "in response to determining" or "in response to detecting ". Similarly, the phrase "if determined" or "if [the described condition or event] is detected" may be construed, depending on the context, to mean "once determined" or "in response to the determination" or "once detected [the described condition or event] ]” or “in response to detection of [described condition or event]”.

In addition, in the description of the specification and appended claims of the present application, the terms "first", "second", "third" and so on are only used to distinguish descriptions, and should not be understood as indicating or implying relative importance.

Reference to "one embodiment" or "some embodiments" or the like in the specification of the present application means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in other embodiments," etc. in various places in this specification are not necessarily All refer to the same embodiment, but mean "one or more but not all embodiments" unless specifically stated otherwise. The terms "including", "comprising", "having" and variations thereof mean "including but not limited to", unless specifically stated otherwise.

Brief Introduction of Invention Concept

The blood flow numerical simulation method provided in the embodiment of the present application is suitable for analyzing the blood flow in the blood vessel. The embodiment of the present application does not limit the specific application scenarios, and the method provided in the embodiment of the present application can determine the blood flow in the blood vessel. The boundary conditions of the fluid governing equations, and the application scenarios in which the numerical simulation results of blood flow are obtained by solving them all belong to the protection scope of the present application. In a possible application scenario, the blood flow numerical simulation method provided in the embodiment of the present application may be applied to blood vessels in human organs. Exemplarily, the blood vessels in human organs may be cerebral blood vessels. In the embodiment of the present application, the blood flow numerical simulation method will be specifically described by taking the cerebral blood vessel as an example.

Fig. 1 is a schematic flow chart of the blood flow numerical simulation method provided in the embodiment of the present application. The method provided in the embodiment of the present application will be described below in conjunction with Fig. 1. This blood flow numerical simulation method includes the following steps:

Step 101: Obtain a three-dimensional model of the blood vessel to be evaluated and blood flow velocity measurement data, the blood flow velocity measurement data includes blood flow velocity of multiple target points in the three-dimensional model, and the three-dimensional model includes multiple blood vessel regions.

The embodiment of the present application does not limit the method for obtaining the three-dimensional model. In a possible implementation manner, tomographic image data of the blood vessel to be evaluated is obtained, and then the three-dimensional model of the blood vessel to be evaluated is obtained according to the tomographic image data. Exemplarily, the tomographic image data is computer tomography (Computed Tomography, CT) image data.

After obtaining the tomographic image data, in order to construct a three-dimensional model through the tomographic image data, further processing of the image data is required. Taking cerebrovascular as an example, due to the many branches of cerebral vascular and the limited accuracy of imaging data of medical tomography, it is impossible to realize the reconstruction of distal blood vessels with too small diameter. Therefore, the reconstructed 3D model mainly includes large-diameter Blood vessel.

It is worth noting that the reconstructed 3D model of the blood vessel should include target points for obtaining blood flow velocity measurement data. Wherein, the blood flow velocity measurement data described in the embodiments of the present application refers to valid data obtained after actual measurement of the blood vessel to be evaluated by means of instruments and measurement methods. The target point is a point in the blood vessel to be evaluated, where effective data can be obtained from blood flow velocity measurement data. Exemplarily, FIG. 2 is a schematic diagram of the region division of the 3D model and the section of the blood vessel where the target point is provided in the embodiment of the present application. The 3D model will be described exemplarily below in conjunction with FIG. 2 . The three-dimensional model shown in FIG. 2 is a three-dimensional model of cerebral arteries, which includes left and right middle cerebral arteries and anterior arteries, and S ₁ , S ₂ , S ₃ and S ₄ are four target points.

In the process of blood flow, the blood flows from the thicker blood vessels at the bottom of the 3D model to the thinner blood vessels at the top of the 3D model. Therefore, in Figure 2, the bottom is the inlet of the 3D model, and the top is the outlet. Exemplarily, FIG. 2 includes an inlet A and an outlet B, blood flows into the three-dimensional model through the inlet A, and flows out of the three-dimensional model through the outlet B. Similarly, according to the flow direction of blood, it can be seen that the three-dimensional model in Fig. 2 includes two inlets and multiple outlets.

The present application also does not limit the technical means for constructing a three-dimensional model based on the tomographic image data. In a possible implementation, the three-dimensional model is constructed through Mimics or Geomagic software.

It should be noted that, through the construction of the three-dimensional model, at least one of the radius, diameter or cross-sectional area of the blood vessel in the three-dimensional model can be calculated.

It can be seen from FIG. 2 that the embodiment of the present application divides multiple blood vessel regions in the three-dimensional model, and the determination of different blood vessel regions will be used in subsequent steps to distribute outlet resistance according to the flow rate. Therefore, the determination of the vessel area is based on the position of the target point. Specifically, the total blood flow in the blood vessel area can be determined through the blood flow velocity measurement data at the target point.

Take Figure 2 as an example, which includes three blood vessel regions 1, 2 and 3.

The blood flow velocity and cross-sectional area of the target point are known, so the blood flow rate of the target point can be calculated. In addition, there is a law of conservation of flow in blood vessels, that is, the sum of the blood flow flowing into the bifurcation of the blood vessel is equal to the sum of the blood flow flowing out. As shown in Figure 2, blood flows into vascular region ₁ from S1, the total blood flow in vascular region ₁ is the blood flow of S1, blood flows into vascular region ₂ from S2 and S3, and the total blood flow in vascular region ₂ It is the sum _of the blood flow of S2 and S3, the blood flows from S4 into the vascular area ₃ , and the total blood flow in the vascular area ₃ is the blood flow of S4 _. FIG. 2 is only an exemplary description. When a certain target point exists in the three-dimensional model, a similar method can be used to determine the blood vessel region in the three-dimensional model. The embodiment of the present application does not limit the acquisition method of blood flow velocity measurement data. Taking cerebrovascular as an example, in a possible implementation manner, the blood flow velocity measurement data may include transcranial Doppler ultrasound (Transcranial Doppler, TCD) data . TCD uses the natural weak part of the human skull as the ultrasonic incident point, and uses the Doppler effect to obtain the blood flow velocity of the target point. Therefore, the TCD method can obtain the target point of the blood flow velocity is limited.

It is worth noting that since the method used in the embodiment of the present application is the CFD method, the blood flow rate required in the embodiment of the present application is the specific data that can reflect the change of the blood flow rate with time, as well as the cycle time. The period length can be understood as the time period during which the blood flow rate changes, and the blood flow rate that needs to be measured in the embodiment of the present application is the blood flow rate within one or more period periods. Exemplarily, Fig. 3 is a transcranial Doppler ultrasound image provided by the embodiment of the present application, which includes the blood flow velocity of four target points S ₁ , S ₂ , S ₃ and S ₄ , where the horizontal axis is time and the vertical axis is the blood flow velocity, and it can be seen from the waveform in FIG. 3 that the blood flow velocity includes four cycles. In the embodiment of the present application, the blood flow velocity corresponding to the four target points shown in the three-dimensional model in FIG. 2 is acquired.

Step 102: Determine the outlet resistance of each blood vessel region according to the blood flow velocity at multiple target points and the pressure difference at the inlet of the three-dimensional model.

In a possible implementation, step 102 includes the following steps. FIG. 4 is a schematic flowchart of a method for determining the outlet resistance in a vascular region provided by an embodiment of the present application. These steps will be described below in conjunction with FIG. 4 :

Step 201: Obtain the blood flow of each target point according to the blood flow velocity of each target point.

As mentioned above, the blood flow velocity at the target point can be obtained in step 101, and the blood flow refers to the blood volume flowing through a certain section of the blood vessel per unit time, so the blood flow at the target point can be calculated. Exemplarily, in the three-dimensional model shown in FIG. 2 , the corresponding blood flow can be calculated according to the blood flow velocity and cross-sectional area of the target points S ₁ , S ₂ , S ₃ and S ₄ .

Step 202: Determine the blood flow ratio of each blood vessel region relative to the three-dimensional model according to the blood flow at multiple target points.

When determining the flow ratio of each vascular region, it is necessary to first confirm the total blood flow of the vessel to be evaluated. In a possible implementation manner, the corresponding blood flow velocity at the inlet of the three-dimensional model is confirmed by the TCD method, and the total blood flow flowing into the blood vessel to be evaluated is calculated.

Subsequently, the blood flow of each blood vessel region is determined according to the blood flow of the target point. Exemplarily, the blood flow of blood vessel region ₁ in FIG. 2 is the blood flow of S1.

After obtaining the total blood flow and the blood flow of each vascular region, the blood flow ratio of each vascular region can be obtained.

Step 203: Determine the outlet resistance of each vascular region according to the blood flow ratio of each vascular region relative to the three-dimensional model and the pressure difference at the inlet of the three-dimensional model.

In a possible implementation, step 203 includes the steps in FIG. 5 . FIG. 5 is a schematic flowchart of determining the outlet resistance according to the blood flow ratio of each vascular region relative to the three-dimensional model provided in the embodiment of the present application. The following combines Figure 5 illustrates these steps:

Step 301: Obtain the total resistance of the three-dimensional model according to the total blood flow of the three-dimensional model and the pressure difference at the inlet of the three-dimensional model.

The confirmation method of the total blood flow was mentioned above, so the pressure difference at the inlet can be obtained, so as to confirm the total resistance of the three-dimensional model through Ohm's law. Among them, Ohm's law means that the blood flow is directly proportional to the pressure difference at both ends of the blood vessel, and inversely proportional to the blood flow resistance.

Taking the cerebral blood vessel as an example, since the pressure of the blood vessel at the outlet is relatively stable within a period of time, the pressure of the blood vessel at the outlet can be approximated as a constant when using Ohm's law. Therefore, the total resistance of the three-dimensional model can be calculated by obtaining the pressure difference at the inlet between two different moments and the corresponding blood flow in the three-dimensional model. Specifically, the total resistance of the three-dimensional model refers to the total resistance of all outlets in the three-dimensional model.

In a possible implementation manner, the pressure difference at the inlet uses the pressure difference measured at the left arm or the carotid artery during systole and diastole, which is relatively easy to measure and has high accuracy.

Step 302: For each blood vessel region, according to the blood flow ratio of the blood vessel region to the three-dimensional model and the total resistance of the three-dimensional model, the total resistance of the blood vessel region is obtained.

According to the proportion of blood flow obtained in step 202 and the total resistance of the three-dimensional model obtained in step 301, the total resistance of the blood vessel area can be calculated. Wherein, the total resistance of the vascular region refers to the total resistance of all outlets in a vascular region.

Taking Fig. 2 as an example, it can be seen that different blood vessel regions are in parallel relationship with each other, so the total resistance of each blood vessel region can be calculated according to the parallel relationship of resistance.

Step 303: According to the total resistance of the vascular region and the cross-sectional size of the outlet in the vascular region, obtain the resistance of the outlet in the vascular region.

Specifically, the resistance of outlets in the vascular region here refers to the respective resistance of each outlet in the vascular region.

Exemplarily, suppose there are three blood vessel regions 1, 2 and 3 in a three-dimensional model, and there are 9 outlets in total. Blood vessel region 1 includes outlets 1-3, blood vessel region 2 includes outlets 4-6, and blood vessel region 3 includes outlets 4-6. Exit 7-9 is included, and step 301-step 303 will be described next based on this assumption.

In step 301, according to the total blood flow of the three-dimensional model and the pressure difference at the inlet of the three-dimensional model, the total resistance of the three-dimensional model is obtained, that is, the resistance formed by the parallel connection of outlets 1-9. Step 302 According to the blood flow ratio of the vascular area relative to the 3D model and the total resistance of the 3D model, the total resistance of the vascular area is obtained, that is, the total resistance of each of the vascular areas 1-3, specifically, the total resistance of the vascular area 1 It is the resistance formed by the parallel connection of outlets 1-3. In step 303, the resistance of outlets in the blood vessel area to be determined, taking blood vessel area 1 as an example, is to determine the respective resistances of outlets 1-3, so in step 303, 9 resistances must be determined, corresponding to 9 of the three-dimensional model. export.

It will be appreciated that the larger the cross-sectional dimension of the outlet in the vascular region, the less resistant the outlet is, and the smaller the cross-sectional dimension of the outlet in the vascular region, the greater the resistance of the outlet.

Optionally, the outlet resistance is obtained according to one or more of the radius, diameter, or cross-sectional area of the outlet in the vascular region.

In a possible implementation, the embodiment of the present application obtains the outlet resistance in the blood vessel area through the following formula:

where i denotes the i-th outlet in the vascular region, R _i is the resistance of the i-th outlet, R _T is the total resistance of the vascular region, ri is the radius of the _i -th outlet, and m is the number of outlets in the vascular region .

It can be seen that the embodiment of the present application determines the proportion of blood flow in the blood vessel area through the blood flow velocity of the target point, calculates the total resistance of the three-dimensional model according to the blood flow and the pressure difference at the entrance, and then allocates the blood vessel area according to the proportion of blood flow Finally, the outlet resistance is determined according to the outlet radius, which improves the accuracy of determining the outlet resistance of the blood vessel.

Step 103: Determine the boundary conditions of the fluid control equation of the blood vessel to be evaluated according to the blood flow velocity measurement data and the outlet resistances in multiple blood vessel regions.

The fluid governing equations are mostly equations coupled by nonlinear partial differential equations in mathematics. Specifically, the flow of fluid is controlled by three basic physical principles, namely, the law of conservation of mass, Newton's second law and the law of conservation of energy. , the equations reflecting the corresponding laws can be understood as fluid governing equations.

The embodiment of the present application does not limit the selection of the fluid control equation. In a possible implementation manner, the fluid control equation is a Navier-Stokes (Navier-Stokes, NS) equation.

Optionally, the blood in the blood vessel is approximated as an incompressible Newtonian fluid. Among them, the incompressible fluid refers to the fluid whose density does not change during the flow process, and the Newtonian fluid refers to the shear stress generated between two layers of parallel flowing liquid adjacent to the fluid is proportional to the velocity gradient perpendicular to the flow direction of fluid. Under this approximation, the non-steady-state incompressible NS equation can be adopted:

是血流速度u相对于时间t的偏导数，ρ是血液的密度，

是哈密顿算子，σ是柯西应力张量。Ω是NS方程的空间域，即三维模型所处的空间，(0,T]是NS方程的时间域，T是周期时长，σ的计算满足下式：Among them, u is the blood flow velocity, t is the time,

is the partial derivative of blood velocity u with respect to time t, ρ is the density of blood,

is the Hamiltonian, and σ is the Cauchy stress tensor. Ω is the space domain of the NS equation, that is, the space where the 3D model is located, (0,T] is the time domain of the NS equation, T is the cycle duration, and the calculation of σ satisfies the following formula:

σ＝-pI+2με(u)

Among them, p is the pressure of the blood vessel, I is a 3×3 unit matrix, μ is the dynamic viscosity, ε(u) is the deformation tensor, and the calculation of ε(u) satisfies the following formula:

Among them, u ^T represents the transpose of u.

It should be understood that among the various physical quantities involved in the above unsteady incompressible NS equation, the blood flow velocity u and the pressure p are unknown quantities in the equation, which are the physical quantities to be solved in the embodiment of the present application.

The outlet resistance in the blood vessel region determined in the embodiment of the present application, that is, R _i , is mainly used to determine the boundary conditions of the fluid control equation. In a possible implementation, each outlet in the blood vessel region is simulated by an elastic cavity model, and the elasticity corresponding to each outlet in each blood vessel region is determined according to the blood flow velocity measurement data and the resistance of the outlet in each blood vessel region parameters of the cavity model.

The elastic cavity model is a method of simulating blood vessels in the human body through a circuit model, which simplifies the local vascular system into resistance elements, compliance elements, and inertial elements. Among them, the resistance element is used to simulate the resistance caused by blood vessels, usually resistance, represented by R; the compliance element, also known as elastic element, is used to simulate the contraction and relaxation of blood vessels, usually capacitance, represented by C; the inertial element is It is used to simulate the inertia of blood flow, usually inductance, represented by L. It is worth noting that resistance elements and compliance elements are usually included in the elastic cavity model, but inertial elements may not be included.

The embodiment of the present application does not limit the selection of the elastic cavity model, and in a possible implementation manner, the outlet of the blood vessel region is simulated by using the three-dimensional elastic cavity model. Fig. 6 is a schematic diagram of a ternary elastic cavity model, and the ternary elastic cavity model will be described below in conjunction with Fig. 6 .

表述为第一阻力，

表述为第二阻力，C_i是动脉顺应性，P_i(t)是压力，具体在本申请实施例中是第i个出口的出口边界压力。As shown in Figure 6, it can be seen that there are two resistance elements and one compliance element. For the convenience of description, the

Expressed as the first resistance,

Expressed as the second resistance, C _i is the arterial compliance, and P _i (t) is the pressure, specifically, in the embodiment of the present application, it is the outlet boundary pressure of the i-th outlet.

In a possible implementation, the parameters of the elastic cavity model are calculated by the following formula:

Wherein, _CT is the total compliance of the vascular region, and in a possible implementation manner, _CT is assumed to be a constant.

和C_i也就是本申请实施例需要确定的弹性腔模型的参数。specific,

and C _i are the parameters of the elastic cavity model that need to be determined in the embodiment of the present application.

After the parameters of the elastic chamber model are obtained, the outlet boundary conditions of the fluid control equation are determined according to the parameters of the elastic chamber model corresponding to each outlet in the vascular region.

In the case where the elastic cavity model adopted in the embodiment of this application is a ternary elastic cavity model, the outlet boundary condition satisfies the following formula:

Among them, P _i (t) is the outlet boundary pressure of the i-th outlet, P _i ^b (t) is the distal pressure at the _i -th outlet, and Qi (t) is the blood flow at the i-th outlet. In one possible implementation, P _i ^b (t) can be assumed to be zero or a constant. In the case that the resistance of each outlet can be determined through step 102, Q _i (t) can be obtained in combination with the aforementioned Ohm's law. Therefore, P _i (t) is an unknown physical quantity in the above outlet boundary conditions.

In the embodiment of the present application, the outlet is simulated by the elastic chamber model, and the parameters of the elastic chamber model are determined by the resistance of the outlet, so as to determine the outlet boundary condition of the fluid control equation and improve the accuracy of the obtained outlet boundary condition.

It is worth noting that if the governing equations are to be solved, the equations also need to have known inlet boundary conditions, wall boundary conditions and initial boundary conditions.

The embodiment of the present application does not limit the determination methods of the inlet boundary condition, the wall surface boundary condition and the initial boundary condition. In a possible implementation, the inlet boundary condition and the wall boundary condition are determined by the following equations:

Wherein, v _I is the inflow velocity at the entrance, Γ _I represents the entrance, and Γ _W represents the wall surface. It should be understood that the wall surface is the vessel wall. In one possible implementation, the inflow velocity at the entrance is obtained by transcranial Doppler ultrasound. In another possible implementation, the total blood flow at the entrance is obtained through the flow conservation law, and then according to the total flow and the entrance The inflow velocity is calculated from the cross-sectional area at the point, and the inflow velocity is calculated by the following formula:

v _I = n·Q/S

where n is the inward normal of the inlet, S is the cross-sectional area of the inlet, and Q is the blood flow at the inlet. In one possible implementation, the initial conditions are determined by the following formula:

u| _t＝0 ＝u ₀ ,Ω

Wherein, u ₀ is the velocity of the blood at the initial time. In one possible implementation manner, u ₀ is assumed to be 0, and in another possible implementation manner, u ₀ may also be assumed to be other constants.

Step 104: Solve the fluid control equation according to the boundary conditions to obtain the blood flow numerical simulation results of the vessel to be evaluated.

In a possible implementation manner, the embodiment of the present application uses a numerical solution method based on finite element analysis for solving the fluid control method. Therefore, the three-dimensional model needs to be divided into multiple grids before performing the solution.

Among them, the finite element analysis method regards the solution domain of the equation as composed of many small interconnected sub-domains, assumes a suitable approximate solution for each unit, and then deduces and solves the total satisfaction conditions of this domain, so as to obtain the solution of the problem untie. When solving the NS equation in the embodiment of the present application, it can also be understood that the entire 3D model is a solution domain, and each grid in the 3D model is a subdomain.

The embodiment of the present application does not limit the parameters of grid division. In a possible implementation manner, the three-dimensional model is divided into unstructured tetrahedral grids. Among them, unstructured means that the internal points in the grid area do not have the same adjacent cells, and tetrahedral means that the shape of each grid is tetrahedral. FIG. 7 is a schematic diagram of grid division provided by the embodiment of the present application. It can be seen that FIG. 7 adopts unstructured tetrahedral grid division.

In a possible implementation, the three-dimensional model is divided into 4.73×10 ⁶ or 2.05×10 ⁷ grids.

Specifically, in the process of dividing the grid, it is necessary to set the parameters required for the division first, and after the division is completed, the grid should be refined and smoothed, and the quality of the grid should be checked in the software.

In one possible implementation, the 3D model is meshed using the ICEM module in ANSYS.

After the grid division is completed, the fluid governing equations are discretized in the time domain and the space domain according to multiple grids to obtain a sparse nonlinear system, and then the sparse nonlinear system is solved according to the boundary conditions.

In a possible implementation, the finite element method is used to discretize the fluid governing equations in the space domain, and the Euler method is used to discretize the fluid governing equations in the time domain. Specifically, the fluid governing equations are discretized in the space domain to the grid in the 3D model mentioned above, and the Euler method is a method for solving iteratively.

Optionally, the fluid governing equations are discretized by the P1-P1 finite original method in the space domain, and the fluid governing equations are discretized by the implicit backward Euler method in the time domain. Wherein, the two P1 respectively mean that the P1 finite element method is used for the blood flow velocity u and the pressure p, specifically, the P1 finite element method refers to the first-order linear discrete.

Specifically, the discretized fluid governing equation is a large sparse nonlinear system.

After completing the discretization of the equations, the fluid governing equations can be solved by computer. In a possible implementation, the Tianhe-2A supercomputer (Tianhe-2A) is used for solving.

In a possible implementation, a Newton-Krylov-Schwarz (Newton-Krylov-Schwarz, NKS) algorithm is used to solve the fluid governing equations.

Specifically, after the sparse nonlinear system is obtained, the sparse nonlinear system can also be further processed through the NKS algorithm before being solved.

Specifically, the NKS algorithm refers to the combination of the Newton algorithm for solving nonlinear equation systems with the Krylov subspace technology to obtain the Newton-Krylov algorithm for solving nonlinear systems. (Newton-Krylov) subspace iteration method, and then combined with Schwarz (Schwarz) preconditioner technique in the iterative process, a method to improve the solvability of the equation system is obtained. The subspace here can be understood as another expression of the subfield in the above-mentioned finite element method.

In the embodiment of the present application, the sparse nonlinear system is processed by the NKS algorithm, which improves the calculation efficiency of the computer for solving the fluid control equation.

After solving the NS equation in the embodiment of the present application, since the blood flow velocity u and the pressure p are unknown parameters in the NS equation, the blood flow velocity u and the pressure p can be directly solved.

On the basis of solving the blood flow velocity u and pressure p, other hydrodynamic parameters of the blood can be calculated based on the fluid mechanics properties of the blood through the blood flow velocity u and pressure p, and the numerical simulation results of blood flow can be obtained. In a possible implementation manner, the shear stress of blood can be calculated, and the shear stress refers to the interaction force between two sides of any section inside an object when it is deformed due to external factors.

Optionally, in order to make the numerical simulation results obtained by solving the fluid governing equations more vivid, the numerical simulation structure can be post-processed, and the numerical simulation results can be expressed in the form of images. In one possible implementation, Paraview software is used for post-processing.

According to the blood flow velocity of the target point and the pressure difference at the inlet of the three-dimensional model, the embodiment of the present application determines the outlet resistance in the blood vessel region, improves the accuracy of determining the outlet resistance, and determines the boundary of the fluid control equation according to the outlet resistance The conditions improve the accuracy of the blood flow numerical simulation results obtained by solving the fluid control equations.

Fig. 8 shows a schematic block diagram of a blood flow numerical simulation device according to an embodiment of the present application. As shown in Figure 8, the device 800 includes:

The first acquisition module 810 is configured to acquire a three-dimensional model of the blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data includes the blood flow velocity of multiple target points in the three-dimensional model; the three-dimensional model includes multiple blood vessel regions;

The first determining module 820 is configured to determine the outlet resistance of each blood vessel region according to the blood flow velocity at multiple target points and the pressure difference at the inlet of the three-dimensional model;

The second determination module 830 is to determine the boundary conditions of the fluid control equation of the blood vessel to be evaluated according to the blood flow velocity measurement data and the outlet resistance in multiple blood vessel regions;

The second obtaining module 840 is configured to solve the fluid control equation according to the boundary conditions, and obtain the blood flow numerical simulation result of the blood vessel to be evaluated.

In a possible implementation manner, the first determining module 820 is configured to:

The blood flow of each target point is respectively obtained according to the blood flow velocity of each target point;

According to the blood flow of multiple target points, determine the blood flow ratio of each vascular area relative to the three-dimensional model;

According to the blood flow ratio of each blood vessel region relative to the three-dimensional model and the pressure difference at the inlet of the three-dimensional model, the outlet resistance in each blood vessel region is determined.

In a possible implementation manner, the first determining module 820 is configured to:

Obtain the total resistance of the three-dimensional model according to the total blood flow of the three-dimensional model and the pressure difference at the inlet of the three-dimensional model;

For each of the vascular regions, according to the blood flow ratio of the vascular region relative to the three-dimensional model and the total resistance of the three-dimensional model, the total resistance of the vascular region is obtained;

The resistance of the outlet in the vascular region is obtained from the total resistance of the vascular region and the cross-sectional size of the outlet in the vascular region.

In a possible implementation, the fluid governing equation is the Navier-Stokes equation, the boundary conditions include outlet boundary conditions, and the second determination module 830 is used for:

determining the parameters of the elastic cavity model corresponding to each outlet in each vessel region according to the blood flow velocity measurement data and the resistance of the outlet in each vessel region;

According to the parameters of the elastic chamber model corresponding to each outlet in the plurality of vessel regions, the outlet boundary condition of the fluid control equation is determined.

In a possible implementation manner, the second obtaining module 840 is used to:

Divide the 3D model into multiple meshes;

According to multiple grids, the fluid control equations are discretized in the space domain and the time domain respectively, and a sparse nonlinear system is obtained;

Solve sparse nonlinear systems subject to boundary conditions.

In a possible implementation manner, the second obtaining module 840 is used to:

The Newton-Krylov-Schwartz algorithm is used to solve the fluid governing equations.

In a possible implementation manner, the first acquiring module 810 is configured to:

Obtain tomographic image data of the blood vessel to be evaluated;

According to the tomographic image data, a three-dimensional model of the blood vessel to be evaluated is obtained.

FIG. 9 is a schematic structural diagram of a blood flow numerical simulation device provided in an embodiment of the present application. As shown in FIG. 9 , the blood flow numerical simulation device 900 includes: at least one processor 90 (only one is shown in FIG. 9 ), a processor, a memory 91, and stored in the memory 91 and can be used in the at least one processor. A computer program 92 running on 90, when the processor 90 executes the computer program 92, it is used to realize the steps in any of the above embodiments of the blood flow numerical simulation method (such as the method in FIG. 1 ).

The so-called processor 90 can be a central processing unit (Central Processing Unit, CPU), and the processor 90 can also be other general processors, a digital signal processor (Digital Signal Processor, DSP), an application specific integrated circuit (Application Specific Integrated Circuit , ASIC), off-the-shelf programmable gate array (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor, or the processor may be any conventional processor, or the like.

The memory 91 may be an internal storage unit of the device 900 in some embodiments, such as a hard disk or memory of the blood flow numerical simulation device 900 . The memory 91 may also be an external storage device of the device 900 in other embodiments, such as a plug-in hard disk equipped on the device 900, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, flash memory card (Flash Card), etc. Further, the memory 91 may also include both an internal storage unit of the apparatus 900 and an external storage device. The memory 91 is used to store operating system, application program, boot loader (BootLoader), data and other programs, such as the program code of the computer program. The memory 91 can also be used to temporarily store data that has been output or will be output.

Those skilled in the art can clearly understand that for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used for illustration. In practical applications, the above-mentioned functions can be assigned to different functional units, Completion of modules means that the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment may be integrated into one processing unit, or each unit may exist separately physically, or two or more units may be integrated into one unit, and the above-mentioned integrated units may adopt hardware It can also be implemented in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the protection scope of the present application. For the specific working process of the units and modules in the above system, reference may be made to the corresponding process in the foregoing method embodiments, and details will not be repeated here.

The embodiment of the present application also provides a computer-readable storage medium, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in each of the foregoing method embodiments can be realized.

An embodiment of the present application provides a computer program product. When the computer program product runs on a blood flow numerical simulation device, the blood flow numerical simulation device can realize the steps in the above-mentioned various method embodiments when executed.

If the integrated unit is realized in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the procedures in the methods of the above embodiments in the present application can be completed by instructing related hardware through computer programs, and the computer programs can be stored in a computer-readable storage medium. The computer program When executed by a processor, the steps in the above-mentioned various method embodiments can be realized. Wherein, the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file or some intermediate form. The computer-readable medium may at least include: any entity or device capable of carrying computer program codes to a photographing device/terminal device, a recording medium, a computer memory, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium. Such as U disk, mobile hard disk, magnetic disk or optical disk, etc. In some jurisdictions, computer readable media may not be electrical carrier signals and telecommunication signals under legislation and patent practice.

Claims (10)

1. A numerical simulation method for blood flow, comprising: Acquiring a three-dimensional model of the blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data includes blood flow velocity at multiple target points in the three-dimensional model; the three-dimensional model includes multiple blood vessel regions; determining an outlet resistance in each of the vascular regions based on the blood flow velocity at the plurality of target points and the pressure difference at the inlet of the three-dimensional model; determining the boundary conditions of the fluid control equation of the vessel to be evaluated according to the blood flow velocity measurement data and the outlet resistances in a plurality of the vessel regions; Solving the fluid control equation according to the boundary conditions to obtain a blood flow numerical simulation result of the blood vessel to be evaluated. 2. The method according to claim 1, characterized in that, according to the blood flow velocity of the plurality of target points and the pressure difference at the inlet of the three-dimensional model, the resistance of the outlet in each of the blood vessel regions is determined ,include: Obtaining the blood flow of each of the target points according to the blood flow velocity of each of the target points; determining the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model according to the blood flow at multiple target points; The outlet resistance of each of the blood vessel regions is determined according to the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model and the pressure difference at the inlet of the three-dimensional model. 3. The method according to claim 2, wherein, according to the blood flow ratio of each of the blood vessel regions relative to the three-dimensional model and the pressure difference at the entrance of the three-dimensional model, each Outlet resistance in the vascular region, including: Obtaining the total resistance of the three-dimensional model according to the total blood flow of the three-dimensional model and the pressure difference at the inlet of the three-dimensional model; For each of the blood vessel regions, according to the ratio of blood flow of the blood vessel region to the three-dimensional model and the total resistance of the three-dimensional model, the total resistance of the blood vessel region is obtained; and according to the total resistance of the blood vessel region The resistance and the cross-sectional dimension of the outlet in the vascular region obtain the resistance of the outlet in the vascular region. 4. according to the method described in any one in claim 1-3, it is characterized in that, described fluid control equation is Navier-Stokes equation, and described boundary condition comprises outlet boundary condition, and described according to described The blood flow velocity measurement data and the resistance of outlets in the plurality of vascular regions determine the boundary conditions of the fluid control equation of the blood vessel to be evaluated, including: determining the parameters of the elastic chamber model corresponding to each outlet in each of the blood vessel regions according to the blood flow velocity measurement data and the resistance of the outlet in each of the blood vessel regions; The outlet boundary condition of the fluid control equation is determined according to the parameters of the elastic chamber model corresponding to each outlet in the multiple blood vessel regions. 5. The method according to any one of claims 1-3, wherein said solving the fluid governing equations according to the boundary conditions comprises: dividing the three-dimensional model into a plurality of grids; discretizing the fluid governing equations in the space domain and the time domain respectively according to the plurality of grids to obtain a sparse nonlinear system; The sparse nonlinear system is solved according to the boundary conditions. 6. The method according to claim 5, wherein said solving said fluid governing equations according to said boundary conditions comprises: The Newton-Krylov-Schwartz algorithm is used to solve the fluid governing equations. 7. The method according to any one of claims 1-3, wherein said obtaining a three-dimensional model of a blood vessel to be evaluated comprises: Acquiring tomographic image data of the vessel to be evaluated; Acquiring a three-dimensional model of the blood vessel to be evaluated according to the tomographic image data. 8. A numerical simulation device for blood flow, comprising: A first acquisition module, configured to acquire a three-dimensional model of a blood vessel to be evaluated and blood flow velocity measurement data; the blood flow velocity measurement data includes blood flow velocity at multiple target points in the three-dimensional model; the three-dimensional model includes multiple blood vessel regions; A first determining module, configured to determine the outlet resistance of each of the blood vessel regions according to the blood flow velocity of the plurality of target points and the pressure difference at the inlet of the three-dimensional model; The second determination module is to determine the boundary conditions of the fluid control equation of the blood vessel to be evaluated according to the blood flow velocity measurement data and the resistance of outlets in a plurality of the blood vessel regions; The second acquisition module is configured to solve the fluid control equation according to the boundary conditions, and acquire the blood flow numerical simulation results of the blood vessel to be evaluated. 9. A blood flow numerical simulation device, comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, characterized in that, when the processor executes the computer program, it realizes The method according to any one of claims 1 to 7. 10. A computer-readable storage medium storing a computer program, wherein the computer program implements the method according to any one of claims 1 to 7 when executed by a processor.

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